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General approach for constructing the computer models of the multibody system dynamics with unilateral constraints and friction is under consideration. Base dynamical abstractions, classes, are described which provide a model building using object-oriented paradigm for the design of dynamic objects virtual prototypes. Contact tracking block is the most important one of any algorithm for simulation the mechanical contact. This block provides permanent computations of the contact point/patch where the process of bodies mechanical interaction takes place. A general formulation of contact in algebraic and/or differential forms is under analysis. The omni directional wheel dynamical testbench is under construction then. This model is built in a way such that the wheel disc equipped by rollers along its rim keeps its vertical orientation permanently. Such an arrangement of the virtual testbench provides indeed the simulation of the wheel motion like it is a part of any virtual omni vehicle. Using the omni wheel permanent vertical orientation we are able to build up an efficient algorithm for contact tracking between the roller and the floor. The case of so-called angled (being preliminarily rotated) rollers is also included. The angle of roller inclination to the wheel plane is possible to be varied, as a parameter of the dynamical problem, in frame of wide range of its values. This approach is a natural generalization of its previous version which was implemented for the case of zero angle of the roller prerotation.